Description of fast matrix multiplication algorithm: ⟨3×7×8:126⟩

Algorithm type

12X2Y3Z2+30X2Y2Z2+4XY4Z+12X2YZ2+24XY3Z+24XY2Z+20XYZ12X2Y3Z230X2Y2Z24XY4Z12X2YZ224XY3Z24XY2Z20XYZ12*X^2*Y^3*Z^2+30*X^2*Y^2*Z^2+4*X*Y^4*Z+12*X^2*Y*Z^2+24*X*Y^3*Z+24*X*Y^2*Z+20*X*Y*Z

Algorithm definition

The algorithm ⟨3×7×8:126⟩ is the (Kronecker) tensor product of ⟨1×1×2:2⟩ with ⟨3×7×4:63⟩.

Algorithm description

Algorithm symmetries

The following group of 8 isotropies acts as a permutation group on algorithm tensor representation:

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.


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